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29 problems tagged with Simple harmonic oscillation in Oscillations
P0679
Intermediate Mechanics › OscillationsMinimizing a Physical Pendulum's Period
A stick of length L = 1.85 m oscillates as a physical pendulum. The pivot point O is a distance x from the stick's center of mass.
- What value of distance x gives the least period?
- What is that least period?
P0680
Intermediate Mechanics › OscillationsTorsional Oscillation of a Spring-Coupled Cube
A 3.00 kg cube with edge lengths d = 6.00 cm is mounted on an axle through its center. A spring (k = 1200 N/m) connects the cube's upper corner to a rigid wall. Initially, the spring is horizontal and at its rest length. The cube is then rotated 3° and released.
P0681
Intermediate Mechanics › OscillationsOscillation of a Spring-Coupled Rod
An overhead view shows a long uniform rod of mass 0.600 kg free to rotate in a horizontal plane about a vertical axis through its center. A spring with force constant k = 1850 N/m is connected horizontally between one end of the rod and a fixed wall. In equilibrium, the rod is parallel to the wall, and the spring is perpendicular to the rod.
P0682
Intermediate Mechanics › OscillationsMinimum Period of a Pivoted Rod
A pendulum is formed by pivoting a long thin rod about a point on the rod. In a series of experiments, the period is measured as a function of the distance $x$ between the pivot point and the rod's center. The rod's length is $L = 2.20$ m and its mass is $m = 22.1$ g.
- What is the minimum period?
- If $x$ is chosen to minimize the period and then $L$ is increased, does the period increase, decrease, or remain the same?
- If, instead, $m$ is increased without $L$ increasing, does the period increase, decrease, or remain the same?
P0683
Intermediate Mechanics › OscillationsPhysical Pendulum with a Torsion Spring
A 2.50 kg disk of diameter $D = 42.0$ cm is supported by a rod of length $L = 76.0$ cm and negligible mass that is pivoted at its end.
- With the massless torsion spring unconnected, what is the period of oscillation?
- With the torsion spring connected, the rod is vertical at equilibrium. What is the torsion constant of the spring if the period of oscillation has been decreased by 0.500 s?
P0686
Intermediate Mechanics › OscillationsAngular Frequency of an Oscillating Wheel
A wheel is free to rotate about its fixed axle. A spring is attached to one of its spokes a distance $r$ from the axle, as shown in the figure.
- Assuming that the wheel is a hoop of mass $m$ and radius $R$, what is the angular frequency $\omega$ of small oscillations of this system in terms of $m, R, r,$ and the spring constant $k$?
- What is $\omega$ if $r=R$?
- What is $\omega$ if $r=0$?
P0687
Beginner Mechanics › OscillationsVibrating Stone on a Vertical Spring
A stone of mass $m$ is attached to the bottom of a vertical spring and set vibrating. If the maximum speed of the stone is $v_{max}$ and the period is $T$, find the following.
- The spring constant of the spring.
- The amplitude of the motion.
- The frequency of oscillation.
P0688
Beginner Mechanics › OscillationsBlock-Spring Oscillator Period and Frequency
An oscillating block-spring system takes 0.75 s to begin repeating its motion.
- Find the period.
- Find the frequency in hertz.
- Find the angular frequency in radians per second.
P0689
Beginner Mechanics › OscillationsMeter Stick Physical Pendulum Pivot Distance
A physical pendulum consists of a meter stick that is pivoted at a small hole drilled through the stick a distance $d$ from the 50 cm mark. The period of oscillation is 2.5 s.
P0678
Intermediate Mechanics › OscillationsSwinging Rod as a Physical Pendulum
A thin uniform rod (mass = 0.50 kg) swings about an axis that passes through one end of the rod and is perpendicular to the plane of the swing. The rod swings with a period of 1.5 s and an angular amplitude of 10°.
- What is the length of the rod?
- What is the maximum kinetic energy of the rod as it swings?
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